How does the LS3 measure the force?

The lineScale works by the principle of material micro deformation: Wikipedia – Strain Gauge

In short, and simplified:
The strain gauges that are glued to the inside of the aluminum body measure how much the aluminum stretches (nanometers).
By means of the calibration values the electronics then calculate how high the force must be to account for this stretch.
This value is then displayed on the screen in the selected load unit.